Reapplying for the same role after rejection?

Hi, about 5/6 months ago I went through the process with a large PE fund, I passed all of the rounds including the modelling test and numerous interviews, and made it to the final round which was a one to one with the head of the team.

The final round was actually very chill and was just a chat with the head of the team and unfortunately I got rejected without any feedback other than they’ve decided to give another candidate the offer. I thought it went well, conversation flowed and no awkward / bad moments. All that hard work for nothing. I tried emailing my previous interviewers for feedback but didn’t get a response.

Anyways it’s now been 5/6 months and I’ve just been headhunted by a different recruiter for the same role in the same team who said that they had someone join 4/5 months ago (the position I originally applied to) and that due to a strong pipeline they’re making an additional hire now.

How should I approach this ? Thanks